A Subtractor is a digital logic circuit in electronics that performs the operation of subtraction of two number. Subtractors are classified into two types: half subtractor and full subtractor. The **half subtractor** (HS) circuit has two inputs: A and B, which subtract two input binary digits and generate two binary outputs i.e. borrow and difference.

### Truth table of half subtractor

The truth table of the HS Circuit is shown in figure 2.

### Implementation of HS

Logical expression for difference,

Logical expression for borrow,

The HS works by combining the operations of basic logic gates, with the simplest form using only an **XOR**, one **NOT** and an **AND** gate.

**Note:**

1. Minimum number of NAND Gate required implementing HS = 5

2. Minimum number of NOR Gate required implementing HS = 5

3. Number of Multiplexers required implementing HS = 3 (2×1 Multiplexer)

4. HS can be implemented by a combination of one **2×4 decoder** and one **OR** gate.